Check Joint Binary Probabilities

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Description

The main diagonal elements commonprob[i,i] are interpreted as probabilities p(A_i) that a binary variable A_i equals 1. The off-diagonal elements commonprob[i,j] are the probabilities p(A_iA_j) that both A_i and A_j are 1.

This programs checks some necessary conditions on these probabilities which must be fulfilled in order that a joint distribution of the A_i with the given probabilities can exist.

The conditions checked are

0 <= p(A_i) <= 1

max(0, p(A_i)+p(A_j)-1) <= p(A_iA_j) <= min(p(A_i), p(A_j)), i != j

p(A_i)+p(A_j)+p(A_k)-p(A_iA_j)-p(A_iA_k)-p(A_jA_k) <= 1, i != j, i != k, j != k

Usage

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check.commonprob(commonprob)

Arguments

commonprob

Matrix of pairwise probabilities.

Value

check.commonprob returns TRUE, if all conditions are fulfilled. The attribute "message" of the return value contains some information on the errors that were found.

Author(s)

Andreas Weingessel

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics, http://www.wu-wien.ac.at/am

See Also

simul.commonprob, commonprob2sigma

Examples

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check.commonprob(cbind(c(0.5, 0.4), c(0.4, 0.8)))

check.commonprob(cbind(c(0.5, 0.25), c(0.25, 0.8)))

check.commonprob(cbind(c(0.5, 0, 0), c(0, 0.5, 0), c(0, 0, 0.5)))